[EM] Juho--about unreversed Nash equilibria

[Michael Ossipoff]

Juho says:

I'd still appreciate the "no Nash equilibria problem" to be demonstrated as 
a real life example. Well, maybe you think you already did this :-).

I reply:

As I said, my margins order-reversal example may be the example that you ask 
for. It remains for me to check it, to find out if the B & C voters can save 
B without defensive order-reversal. Maybe so, maybe not. If so, then I’ll 
post an example in which they cannot.

But your smiley suggests that my examples are not what you mean by “real 
life example”s. Well, since margins isn’t in use anywhere, it would be 
difficult to find real life examples. All one can do is show what can 
happen.

Now you’re doubting that the voters will end up at a Nash equilibrium.What 
can I say? Nash equilibria occur and are used in legal systems and 
throughout the animal kingdom. By bees too? Maybe!

If, from a given voting configuration, it’s possible for a group of voters 
to improve their outcome by voting differently, then why shouldn’t they? You 
know, the person who should be expected to defend his claim is the person 
claiming that Nash equilibria won’t matter.

You’re proposing a voting system that will often have situations in which 
the only Nash equilibria, the only stable outcomes, are ones in which people 
order-reverse. Do you realize how far you’re going in order to forgive that 
big fault of margins?

It isn’t as if only a few methods meet Unreversed Nash Equilibrium Criterion 
(URNEC). That criterion is met by wv, Approval, the various other 
point-rating methods (collectively known as Cardinal Ratings, or CR), MDDA, 
MAMPO, and Bucklin.

Methods that fail URNEC?: Plurality, IRV, margins, among others.

Methods that fail URNEC I refer to as “reversed methods”. You advocate a 
reversed method, one in which voting configurations with order-reversal will 
often be the only stable voting configurations.

Mike Ossipoff